Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation

Scientific Reports

Volumn 5, Issue , 2015, Pages

  Pulkkinen, Otto ^a   Metzler, Ralf ^a,b  

^a TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

^b UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BACTERIAL GENE; ENZYME MECHANISM; MICHAELIS MENTEN KINETICS; RESPONSE TIME; SUBSTRATE CONCENTRATION; THEORETICAL MODEL; VALIDITY; CHEMISTRY; ENZYME ACTIVATION; ENZYME SPECIFICITY; ESCHERICHIA COLI; GENE EXPRESSION REGULATION; GENETIC TRANSCRIPTION; GENETICS; KINETICS;

ESCHERICHIA COLI PROTEIN; LAC REPRESSOR; LACI PROTEIN, E COLI;

ENZYME ACTIVATION; ESCHERICHIA COLI; ESCHERICHIA COLI PROTEINS; GENE EXPRESSION REGULATION, BACTERIAL; KINETICS; LAC REPRESSORS; MODELS, THEORETICAL; SUBSTRATE SPECIFICITY; TRANSCRIPTION, GENETIC;

EID: 84949239330     PISSN: None     EISSN: 20452322     Source Type: Journal    
DOI: 10.1038/srep17820     Document Type: Article

References (62)

1. Henri, V. Théorie générale de l'action de quelques diastases. C. R. Acad. Sci. Paris 135, 916-919 (1902).
2. Henri, V. Lois générales de l'action des diastases 1-129 (Hermann, Paris, 1903).
3. Michaelis, L. & Menten, M. L. Die Kinetik der Invertinwirkung. Biochem. Z. 49, 333-369 (1913).
4. Popova, S. V. & Sel'kov, E. E. Generalization of the model of Monod, Wyman and Changeux for the case of reversible monosubstrate reactions. FEBS Lett. 53, 270-273 (1975).
5. Lomholt, M. A., Urbakh, M., Metzler, R. & Klafter, J. Manipulating Single Enzymes by an External Harmonic Force. Phys. Rev. Lett. 98, 168302 (2007).
6. Briggs, G. E. & Haldane, J. B. S. A note on the kinematics of enzyme action. Biochem. J. 19, 338-339 (1925).
7. Rao, C. V. & Arkin, A. P. Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm. J. Chem. Phys. 118, 4999-5010 (2003).
8. Grima, R. Noise-induced breakdown of the Michaelis-Menten equation in steady-state conditions. Phys. Rev. Lett. 102, 218103 (2009).
9. Bartholomay, A. F. A stochastic approach to statistical kinetics with applications to enzyme kinetics. Biochemistry 1, 223-230 (1962).
10. Kou, S. C., Cherayil, B. J., Min, W., English, B. P. & Xie, X. S. Single-molecule Michaelis-Menten equations. J. Phys. Chem. B 109, 19068-19081 (2005).
11. English, B. P. et al. Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited. Nature Chem. Biol. 2, 87-94 (2006).
12. Moffitt, J. R., Chemla, Y. R. & Bustamante, C. Mechanistic constraints from the substrate concentration dependence of enzymatic fluctuations. Proc. Natl. Acad. Sci. USA 107, 15739-15744 (2010).
13. Grima, R., Walter, N. G. & Schnell, S. Single-molecule enzymology à la Michaelis-Menten. FEBS J. 281, 518-530 (2014).
14. Stéfanini, M. O., McKane, A. J. & Newman, T. J. Single enzyme pathways and substrate fluctuations. Nonlinearity 18, 1575-1595 (2005).
15. Smeach, S. C. & Smith, W. A comparison of stochastic and deterministic models for cell membrane transport. J. Theor. Biol. 42, 157-167 (1973).
16. Qian, H. & Elson, E. L. Single-molecule enzymology: stochastic Michaelis-Menten kinetics. Biophys. Chem. 101-102, 565-576 (2002).
17. Molski, A. Single-molecule Michaelis-Menten kinetics: Effect of substrate fluctuations. Chem. Phys. 352, 277-280 (2008).
18. McAdams, H. H. & Arkin, A. Stochastic mechanisms in gene expression. Proc. Natl. Acad. Sci. USA 94, 814-819 (1997).
19. Thattai, M. & van Oudenaarden, A. Intrinsic noise in gene regulatory networks. Proc. Natl. Acad. Sci. USA 98, 8614-8619 (2001).
20. Swain, P. S., Elowitz, M. B. & Siggia, E. D. Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc. Natl. Acad. Sci. USA 99, 12795-12800 (2002).
21. Paulsson, J. Models of stochastic gene expression. Phys. Life Rev. 2, 157-175 (2005).
22. Kaern, M., Elston, T. C., Blake, W. J. & Collins, J. J. Stochasticity in gene expression: from theories to phenotypes. Nat. Rev. Genet. 6, 451-64 (2005).
23. Toner, D. L. K. & Grima, R. Effects of bursty protein production on the noisy oscillatory properties of downstream pathways. Sci. Rep. 3, 2438 (2013).
24. Lloyd-Price, J., Tran, H. & Ribeiro, A. S. Dynamics of small genetic circuits subject to stochastic partitioning in cell division. J. Theor. Biol. 356, 11-19 (2014).
25. Kallenberg, O. Foundations of Modern Probability 49 (Springer, New York, 2002).
26. Apostol, T. M. Calculus 278-279 (John Wiley & Sons, New York, 1967).
27. Berg, O. G., Winter, R. B. & von Hippel, P. H. How do genome-regulatory proteins locate their DNA target sites? Trends Biochem. Sci. 7, 52-55 (1982).
28. von Hippel, P. H. & Berg, O. G. Facilitated taget location in biological systems. J. Biol. Chem. 264, 675-678 (1989).
29. Slutsky, M. & Mirny, L. Kinetics of protein-DNA interaction: facilitated target location in sequence-dependent potential. Biophys. J. 87, 4021-4035 (2004).
30. Gowers, D. M., Wilson, G. G. & Halford, S. E. Measurement of the contributions of 1D and 3D pathways to the translocation of a protein along DNA. Proc. Natl. Acad. Sci. USA 102, 15883-15888 (2005).
31. Elf, J., Li, G. W. & Xie, X. S. Probing transcription factor dynamics at the single-molecule level in a living cell. Science 316, 1191-1194 (2007).
32. Koslover, E. F., Diaz de la Rosa, M. A. & Spakowitz, A. J. Theoretical and computationsl modeling of target-site search kinetics in vitro and in vivo. Biophys. J. 101, 856-865 (2011).
33. Bauer, M. & Metzler, R. In vivo facilitated diffusion model. PLoS ONE 8, e53956 (2013).
34. Bauer, M., Rasmussen, E. S., Lomholt, M. A. & Metzler, R. Real sequence effects on the search dynamics of transcription factors on DNA. Sci. Rep. 5, 10072 (2015).
35. Pulkkinen, O. & Metzler, R. Distance Matters: The Impact of Gene Proximity in Bacterial Gene Regulation. Phys. Rev. Lett. 110, 198101 (2013).
36. von Hippel, P., Revzin, A., Gross, C. A. & Wang, A. C. Non-specific DNA binding of genome regulating proteins as a biological control mechanism: I. The lac operon: equilibrium aspects. Proc. Natl. Acad. Sci. USA 71, 4808-4812 (1974).
37. Gerland, U., Moroz, J. D. & Hwa, T. Physical constraints and functional characteristics of transcription factor-DNA interaction. Proc. Natl. Acad. Sci. USA 99, 12015-12020 (2002).
38. Stormo, G. D. & Fields, D. S. Specificity, free energy and information content in protein-DNA interactions. Trends Biochem. Sci. 23, 109-113 (1998).
39. Bakk, A. & Metzler, R. In vivo non-specific binding of λ CI and Cro repressors is significant. FEBS Lett. 563, 66-68 (2004).
40. Goel, N. S. & Richter-Dyn, N. Stochastic models in biology. 1-284 (Academic Press, New York, 1974).
41. Shahrezaei, V. & Swain, P. S. Analytical distributions for stochastic gene expression. Proc. Natl. Acad. Sci. USA 105, 17256-17261 (2008).
42. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 2. 40 (John Wiley & Sons, New York, 1971).
43. Saiz, L., Rubi, J. M. & Vilar, M. G. Inferring the in vivo looping properties of DNA. Proc. Natl. Acad. Sci. USA 102, 17642-17645 (2005).
44. Thanbichler, M., Wang, S. C. & Shapiro, L. The bacterial nucleoid: A highly organized and dynamic structure. J. Cell Biochem. 96, 506-521 (2005).
45. Kolesov, G., Wunderlich, Z., Laikova, O. N., Gelfand, M. S. & Mirny, L. A. How gene order is influenced by the biophysics of transcription regulation. Proc. Natl. Acad. Sci. USA 104, 13948-13953 (2007).
46. van den Broek, B., Lomholt, M. A., Kalisch, S. M. J., Metzler, R. & Wuite, G. J. L. How DNA coiling enhances target localization by proteins. Proc. Natl. Acad. Sci. USA 105, 15738-15742 (2008).
47. Lomholt, M. A., van den Broek, B., Kalisch, S. M. J., Wuite, G. & Metzler, R. Facilitated diffusion with DNA coiling Proc. Natl. Acad. Sci. USA 106, 8204-8208 (2009).
48. Bénichou, O., Chevalier, C., Meyer, B. & Voituriez, R. Facilitated diffusion of proteins on chromatin. Phys. Rev. Lett. 106, 038102 (2011).
49. Cottrell, D., Swain, P. S. & Tupper, P. F. Stochastic branching-diffusion models for gene expression. Proc. Natl. Acad. Sci. USA 109, 9699-9704 (2012).
50. Yu, J., Xiao, J., Ren, X., Lao, K. & Xie, X. S. Probing gene expression in live cells, one protein molecular at a time. Science 311, 1600-1603 (2006).
51. Hammar, P. et al. Direct measurement of transcription factor dissociation excludes a simple operator occupancy model for gene regulation. Nature Genet. 46, 405-408 (2014).
52. Sinitsyn, N. A. & Nemenman, I. Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics. IET Syst. Biol. 4, 409-415 (2010).
53. Levine, E. & Hwa, T. Stochastic fluctuations in metabolic pathways. Proc. Natl. Acad. Sci. USA 104, 9224-9229 (2007).
54. Serfozo, R. Introduction to Stochastic Networks. 206-229 (Springer, New York, 1999).
55. Pirone, J. R. & Elston, T. C. Fluctuations in transcription factor binding can explain the graded and binary responses observed in inducible gene expression. J. Theor. Biol. 226, 111-121 (2004).
56. Min, W. et al. When Does the Michaelis-Menten Equation Hold for Fluctuating Enzymes? J. Phys. Chem. B 110, 20093-20097 (2006).
57. Reuveni, S., Urbakh, M. & Klafter, J. Role of substrate unbinding in Michaelis-Menten enzymatic reactions. Proc. Natl. Acad. Sci. USA 111, 4391-4396 (2014).
58. Min, W., Luo, G., Cherayil, B. J., Kou, S. C. & Xie, X. S. Observation of a power-law memory kernel for fluctuations within a single protein molecule. Phys. Rev. Lett. 94, 198302 (2005).
59. Min, W. et al. Fluctuating Enzymes: Lessons from Single-Molecule Studies. Acc. Chem. Res. 38, 923-931 (2005).
60. Di Rienzo, C., Piazza, V., Gratton, E., Beltram, F. & Cardarelli, F. Probing short-range protein Brownian motion in the cytoplasm of living cells. Nature Comm. 5, 5891 (2014).
61. Reverey, J. F. et al. Superdiffusion dominates intracellular particle motion in the supercrowded space of pathogenic Acanthamoeba castellanii. Sci. Rep. 5, 11690 (2015).
62. Gillespie, D. T. Exact Stochastic Simulation of Coupled Chemical Reactions. J. Phys. Chem. 81, 2340-2361 (1977).